A uniform GTD formulation for the diffraction by a wedge with impedance faces

A uniform high-frequency solution is presented for the diffraction by a wedge with impedance faces illuminated by a plane wave perpendicularly incident on its edge. Arbitrary uniform isotropic impedance boundary conditions may be imposed on the faces of the wedge, and both the transverse electric (TE) and transverse magnetic (TM) cases are considered. This solution is formulated in terms of a diffraction coefficient which has the same structure as that of the uniform geometrical theory of diffraction (UTD) for a perfectly conducting wedge. Its extension to the present case is achieved by introducing suitable multiplying factors, which have been derived from an asymptotic evaluation of the exact solution given by Maliuzhinets. When the field point is located on the surface near the edge, a more accurate asymptotic evaluation is employed to obtain a high-frequency expression for the diffracted field, which is suitable for several specific applications. The formulation described in this paper may provide a useful, rigorous basis to search for a more numerically efficient but yet accurate approximation.